Dominions and Primitive Positive Functions

CAMPERCHOLI, MIGUEL

JOURNAL OF SYMBOLIC LOGIC, THE

ASSOC SYMBOLIC LOGIC, INC

Año: 2018 vol. 83 p. 40 - 54

0022-4812

Let A C such that g and g´ agree on A, we have g = g´. Our main theorem states that if K is closed under ultraproducts, then A dominates b relative to K if and only if there is a partial function F definable by a primitive positive formula in K such that F(a1 ,...,an) = b for some a1,...,an in A. Applying this result we show that a quasivariety of algebras Q with an n-ary near-unanimity term has surjective epimorphisms if and only if SPPu(Q_RSI) has surjective epimorphisms. It follows that if F is a finite set of finite algebras with a common near-unanimity term, then it is decidable whether the (quasi)variety generated by F has surjective epimorphisms.